This is a task that you should not tackle. This is a job for a professional with several years in dealing with black bottom pools. Some areas of the country have had good luck with what is known as a no-drain acid wash. Again, here, this is for someone who has done this for a number of years.
The drain - called main drain- is or should be connected with the skimmer Plumbing and that goes to the pump. You should not have to clean the main drain unless you have a massive amount of debris.
Main drains are routinely cleared using a CO2 tank and either a plug adapter or an inflatable canvas bag thingy the name of which escapes me at the moment. Place it in the front port of the skimmer if that is how it is plumbed and open the tank valve full blast. You will either clear the drain or the plug/canvas thingy will come shooting out of the skimmer so don't stick your face over it when opening the valve. If the pool has a separate main drain there will be at least 1 three port valve in front of the pump pot. With the valve pointed in the right direction put the CO2 tank hose with plug or canvas thingy into the suction line and let er rip.
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Where is the drain located? If it is on the wall near the top then you can keep the water in the pool. If it is near the bottom then you may have to drain the pool.
Drain pool and clean with muriatic acid
The closest you can come would be to use a floculent to settle the dirt to the bottom and then vacuum the bottom layer of water to waste.
If you are not worried about the pool floating on a high water table or you have a hydrostatic valve on the bottom. I would drain it clean it and start again.
I don't know about your pool I do know however that most pool don't have a way out for the water other then through the static skimmer. and people often mistake the hydrostatic valve at the bottom of the pool as the pool drain
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Can you remove the bottom drain shut off valve and still blow out a plug the bottom drain on your pool.
If you're trying to clear up a murky pool, then the only option you have is to filter, back-wash, and add more DE and filter, BW, add more DE, until the water is clear.Try to scoop out as much debris out of the water as you can, top and bottom, and keep the bottom drain clear.You may be able to do a partial drain and refill.
There is no filter at the bottom of a pool. Perhaps you are looking at the hydrostatic valve which is there in case your pool is emptied and Will make sure that the pool wont float in ground water.
Why would you drain your pool just becasue the water is hot? Never drain your inground pool unless you have first cut holes in the bottom of the pool to keep it from floating. If the water table in your area is high enough, your inground pool could "float" out of the ground, effectively ruining your pool.
Perhaps it is not a drain but a hydrostatic valve. These are fitted at the bottoms of pools to let ground water that has built up under an empty pool into the pool in order to stop it from floating out of the ground.
You could drain your pool and have it cleaned. Or just have a pool cleaner clean it for you. And next time use chlorine to prevent larvae from hatching in your pool.